arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1504.04686cs.CRcs.DScs.LG
收藏

用于简洁直方图的本地、私有、高效协议

Local, Private, Efficient Protocols for Succinct Histograms

The Pennsylvania State University(宾夕法尼亚州立大学);Boston University(波士顿大学);Harvard University(哈佛大学)

Raef Bassily, Adam Smith

摘要:

我们给出了有效的协议和匹配精度下界的频率估计的局部模型的差分隐私。在这个模型中,个人用户自己随机化他们的数据,将不同的私人报告发送到一个不受信任的服务器,该服务器将这些报告聚集在一起。我们研究的协议,产生一个简洁的直方图表示的数据。一个简洁的直方图是数据中最频繁的项目(通常称为“重打击者”)及其频率估计值的列表;所有其他项目的频率隐式估计为0。如果有$n$用户的项目来自一个大小为$d$的宇宙,我们的协议在$n$和$\log(d)$中以时间多项式运行。以高概率,他们估计每个项目的准确性,直到错误$O\left(\sqrt{\log(d)/(ε^2n)}\right)$,其中$ε$是隐私参数。此外,我们表明,这么多的错误是必要的,无论计算效率,甚至对于简单的设置,只有一个项目出现在数据集中的显着频率。先前用于该任务的方案(Mishra和Sandler,2006; Hsu,Khanna和Roth,2012)要么在$Ω(d)$中运行,要么具有更严重的错误(约为$\sqrt[6]{\log(d)/(ε^2n)}$),并且唯一已知的错误下限是$Ω(1/\sqrt{n})$。我们还将McGregor et al(2010)的结果适用于当地环境。在一个使用公共硬币的模型中,我们展示了每个用户只需要向服务器发送1比特。对于所有已知的本地协议(包括我们的),转换保持计算效率。

英文摘要:

We give efficient protocols and matching accuracy lower bounds for frequency estimation in the local model for differential privacy. In this model, individual users randomize their data themselves, sending differentially private reports to an untrusted server that aggregates them. We study protocols that produce a succinct histogram representation of the data. A succinct histogram is a list of the most frequent items in the data (often called "heavy hitters") along with estimates of their frequencies; the frequency of all other items is implicitly estimated as 0. If there are $n$ users whose items come from a universe of size $d$, our protocols run in time polynomial in $n$ and $\log(d)$. With high probability, they estimate the accuracy of every item up to error $O\left(\sqrt{\log(d)/(ε^2n)}\right)$ where $ε$ is the privacy parameter. Moreover, we show that this much error is necessary, regardless of computational efficiency, and even for the simple setting where only one item appears with significant frequency in the data set. Previous protocols (Mishra and Sandler, 2006; Hsu, Khanna and Roth, 2012) for this task either ran in time $Ω(d)$ or had much worse error (about $\sqrt[6]{\log(d)/(ε^2n)}$), and the only known lower bound on error was $Ω(1/\sqrt{n})$. We also adapt a result of McGregor et al (2010) to the local setting. In a model with public coins, we show that each user need only send 1 bit to the server. For all known local protocols (including ours), the transformation preserves computational efficiency.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑